GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 May 2019, 09:50

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If x and y are positive integers such that the product of x

Author Message
Intern
Joined: 16 Jul 2010
Posts: 9
If x and y are positive integers such that the product of x  [#permalink]

### Show Tags

19 Sep 2010, 06:45
1
00:00

Difficulty:

65% (hard)

Question Stats:

51% (01:20) correct 49% (01:07) wrong based on 41 sessions

### HideShow timer Statistics

If x and y are positive integers such that the product of x and y is prime, what is the units’ digit of 7^x + 9^y ?

(1) 24 < y < 32
(2) x = 1

-----
I get that just from the question stem itself, you know either x or y must be equal to 1, thus B cannot be the answer. I can't figure out how you can tell the units digit of 9 to the Y just from the statement one.

Help?

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/if-x-and-y-ar ... 42992.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Retired Moderator
Joined: 02 Sep 2010
Posts: 759
Location: London
Re: If x and y are positive integers such that the product of x  [#permalink]

### Show Tags

19 Sep 2010, 08:02
Atrain13gm wrote:
If x and y are positive integers such that the product of x and y is prime, what is the units’ digit of 7^x + 9^y ?

(1) 24 < y < 32
(2) x = 1

-----
I get that just from the question stem itself, you know either x or y must be equal to 1, thus B cannot be the answer. I can't figure out how you can tell the units digit of 9 to the Y just from the statement one.

Help?

Since we know xy is a prime, it implies as you rightly pointed that one of them is 1.

(1) This implies y is not 1, hence x must be 1. Also, we know y must be a prime since xy is a prime. So y can only be 29 or 31. Either case, y is odd. What you need to note is that the units digit of 9^{Odd number} is always 9.
So combining with x=1, I know the units digit of the number in question must be 7+9 or 6. Hence, sufficient

(2) Not sufficient, as I know nothing about y

Further explanation
units digits of 9^x
x=1 9
x=2 1
x=3 9
x=4 1
...
The pattern is easy to spot and imagine why it happens. As the last digit is always multiplied by 9, leaving either 1 or 9 itself
_________________
Intern
Joined: 18 Jul 2010
Posts: 40
Re: If x and y are positive integers such that the product of x  [#permalink]

### Show Tags

19 Sep 2010, 08:06
Hi!

(1) We know that 24 < y < 32 hence x = 1 ! As a matter fact, if we want a product to be prime we need to multiply 1 by a prime number. As y is much greater than 1, x = 1. Besides, I just said that has to be a prime number. So y = 29 or 31!
Now let's see how it goes for the unit digit of th power of 9 :

9^0 = 1
9^1 = 9
9^2 = 81
9^3 = 729
9^4 = ...1

so 9^k if k is odd gives the unit digit as 9.... As y = 29 or 31 (odd numbers), (2) is SUFFICIENT

ANS: A.

Hope it's clear.
Director
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 603
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Re: If x and y are positive integers such that the product of x  [#permalink]

### Show Tags

19 Sep 2010, 09:21
interestingly i think but for the fact that 2 is a prime and an even prime at that, we are not able to answer based on (2). so we know x=1, so y has to be prime. all primes are odds (but for 2), if not for that, would we not be able to say 7 + 9^odd = ends in 6
_________________
Consider kudos, they are good for health
Manager
Joined: 20 Jul 2010
Posts: 210
Re: If x and y are positive integers such that the product of x  [#permalink]

### Show Tags

19 Sep 2010, 11:30
when xy is some prime number, either x = 1 or y =1.
1. 24<y<32 ------> x =1 , y = 29 or 31
when y =29----> 7^1 + 9 ^ 29 = 7 + any number ending in 9 ----> unit digit 6
when y = 31 -----> 7^1 + 9 ^ 31 = 7 + any number ending in 9 ----> unit digit 6
1) is sufficient
2) not sufficient
Ans is A
_________________
If you like my post, consider giving me some KUDOS !!!!! Like you I need them
Manager
Joined: 20 Jul 2010
Posts: 210
Re: If x and y are positive integers such that the product of x  [#permalink]

### Show Tags

19 Sep 2010, 11:43
one more thing to add here-----
cyclicity of numbers is always good in GMAT to remember -
any number ending with 0,1,5,6 raised to any power will have same unit digit as the number itself, cyclicity is 1
any number ending with 2,3,7,8 will have cyclicity 0f 4
for example 3^(n+1) will have same unit as 3^(n+5) or 3^(n+9) or so on....
where n >= 0
3 -> 9 -> 27 -> 81 ----
243 -> 729 -> xxx7 -> xxx1 ---
any number ending with 4,9 will have cyclicity of 2
_________________
If you like my post, consider giving me some KUDOS !!!!! Like you I need them
Manager
Joined: 23 Sep 2009
Posts: 108
Re: If x and y are positive integers such that the product of x  [#permalink]

### Show Tags

19 Sep 2010, 16:01
Atrain13gm wrote:
If x and y are positive integers such that the product of x and y is prime, what is the units’ digit of 7^x + 9^y ?

(1) 24 < y < 32
(2) x = 1

-----
I get that just from the question stem itself, you know either x or y must be equal to 1, thus B cannot be the answer. I can't figure out how you can tell the units digit of 9 to the Y just from the statement one.

Help?

My approach was:
1. Y can be either 29 or 31.
Now y^29 or y^31 will always end in 9 and watever the power of X is the units digit is going to be the same.
So A.

2. X=1 is not enough for a conclusion.
_________________
Thanks,
VP
Joined: 19 Feb 2010
Posts: 334
Re: If x and y are positive integers such that the product of x  [#permalink]

### Show Tags

17 Oct 2010, 04:23
The good thing is that 9^y when y is a prime number greater than 2, since all the primes greater than 2 are odd, the digit will always be 9.

So in the statement 1 it doesn't matter whether y is 29 or 31, we just need to know that y is not 2. Any range that doesn't contain 2 will be good.
Manager
Joined: 25 Aug 2010
Posts: 62
Re: If x and y are positive integers such that the product of x  [#permalink]

### Show Tags

20 Oct 2010, 19:17
good one.... ans : A
Math Expert
Joined: 02 Sep 2009
Posts: 55150
Re: If x and y are positive integers such that the product of x  [#permalink]

### Show Tags

21 Aug 2017, 05:38
[quote="Atrain13gm"]If x and y are positive integers such that the product of x and y is prime, what is the units’ digit of 7^x + 9^y ?

(1) 24 y is not equal to 1, thus y must be a prime number and x must be equal to 1. Only primes between 24 and 32 are 29 and 31, so y is either 29 or 31. Now, the units digit of 9^odd is 9, thus the units’ digit of 7^1 + 9^odd is 7+9=6. Sufficient.

(2) x = 1 --> y can be ANY prime number. If x=1 and y=2, then the units’ digit of 7^x + 9^y is 8, but if x=1 and y is any other prime then the the units’ digit of 7^x + 9^y is 6. Not sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/if-x-and-y-ar ... 42992.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: If x and y are positive integers such that the product of x   [#permalink] 21 Aug 2017, 05:38
Display posts from previous: Sort by